Selective ray visibility
One possibly solution to to render the image twice - once with the Envionment and the other without the environment - and then use the compositor to combine the images, using the render without the environment for the chosen object.

To demonstrate, consider the following scene :



The cube is set to emissive (to reflect in the surfaces of the other objects), Suzanne is reflective, as are the two spheres. The left-hand sphere will be the one that doesn't reflect the environment; to indicate this, its object Pass Index has been set to '1' - the other sphere (and all other objects) have been left with Pass Index set to '0'. The environment has been set to an HDR image.

In order to render the scene twice, we can add an additional render layer :



One render layer should have Use Environment enabled and the other should have Use Environment disabled. Ensure to enable the Object Index pass - this will give us access to the object Pass Index in the compositor.

Setup the Compositor nodes as follows :

 

The IndexOB is used to generate a mask to pick out the object set to Pass Index of 1 (the left-hand sphere). The two rendered (one with and one without the environment) are mixed together based on this mask so that the 'without environment' image shows where one sphere is and the 'with environment' shows for the rest of the render. The Dilate/Erode node allow you to control the blending at the edges of the transition to remove any harse artifacts.

This produces the following result with the left-hand sphere showing all reflections except the environment :